1. Fish farms raise fish in large tanks from juvenile up through the adult stage. The fish are then sold by weight to the second tier restaurant suppliers. The live fish vary in size with a mean weight of 2.4 Kg and standard deviation of 0.2 Kg.

a) If the standard order is 10 fish, then what is the model that can be used to describe the total weight of a standard order of fish?

b) Do you need any assumptions (perhaps something about the fish, or the process) to answer part a) above?

c) Estimate the proportion of fish in a standard order that might weigh less than 2Kg

2. Clean dry rice ready for portioning into bags is prepared by the ton. In the commercial process, each bag of rice is weighed as it comes to the end of the line. The bags are slightly overfilled to allow for random variations in the packaging. The weight of a bag of rice is designed to be 1.02Kg with a standard deviation of 10g (0.010 Kg). You may assume a normal distribution for the weights of bags under these conditions.

1. Suppose the process will automatically shut down if a bag at the end of the line weighs less than 1Kg. What is the chance of a Type I error using this system? (Use your z tables)
2. Briefly describe the Type I error in part a) above. What would happen?

3. A survey of 200 grocery store customers was made to determine the proportion of customers that buy no-name (reduced price) brands. It was reported with 95% confidence that 70.8876% < < 74.4970%

a) Explain carefully what this statement means.

b) Compute the estimated standard error

b) If the survey had included 1500 customers, what would happen to the range?

c) What should you assume about the survey when you answer the above questions?

4. Aptitude tests measure a person's ability or skill in a field of knowledge.Aptitude tests are only an approximation of a person's probability to succeed in a given activity. Taken long term over all careers, Aptitude tests have shown a normal distribution of scores for any single career. Suppose a company only wants to hire people with Aptitude scores greater than 180 points.

a) Should the company use a that is greater than 180 or less than 180 in the null hypothesis for a job applicant? Briefly explain your response.

b) Assume that = 20 for the Aptitude scores. If the company set H₀; 180 then for approximately which test scores could they reject H₀ ? (i.e. what test scores would cause them to reject the null hypothesis?)